Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
Slope Distance to Horizontal Distance: FE Civil practice problem 2
For the Summit Road trunk sewer crossing, a design checker preparing an agency resubmittal package reduces a slope distance of 355 ft measured at vertical angle 9 degrees. What horizontal distance is obtained?
- A206.15 ft
- B259.37 ft
- C350.63 ft
- D314.40 ft
Show the answer and worked solution
Answer: C — 350.63 ft
Worked solution
- Step 1. Use horizontal projection
H = S cos theta
H = 355 cos(9 deg) = 350.63 ft
Why the other choices are wrong
- Choice A
- This total sits about 41% below the correct value, and no single sine-for-cosine swap, complementary-angle slip, or degree-radian mix-up reproduces it from H = 355 * cos(9 deg); the correct horizontal distance is simply 355 * cos(9 deg) = 350.63 ft.
- Choice B
- This result sits about 26% below the correct value, far beyond what a cosine-sine mix-up, a degree-radian slip, or a complementary-angle substitution could generate from H = 355 * cos(9 deg); the correct horizontal distance is 355 * cos(9 deg) = 350.63 ft.
- Choice D
- This figure runs about 10% below the correct value, and swapping to sine, using the complementary angle (90 - 9 deg), or leaving 9 deg unconverted to radians all fail to reproduce it from H = 355 * cos(9 deg); the horizontal distance still equals 355 * cos(9 deg) = 350.63 ft.